It can actually be either. The currently locked servers are..

Behemoth
Phoenix
Odin
Shiva
Moogle
Ultros
Cactuar
Cerberus
Ragnarok
Diabolos
Gilgamesh
Leviathan
Balmung
Excalibur
Hyperion
Tonberry
Mandragora
Bahamut
Chocobo

However, even if a server has character creation unlocked, if the server is full, you still can't make one.

Last time I checked, there were zero EU or NA servers to make characters on. Zero!

Most or all of the servers should have character creation unlocked at some point, since right now the max population number has been cut back.